Isolated points of spectrum of k-quasi-*-class A operators

Salah Mecheri

Displaying similar documents to “Isolated points of spectrum of k-quasi-*-class A operators”

A remark on the range of elementary operators

Said Bouali, Youssef Bouhafsi (2010)

Czechoslovak Mathematical Journal

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Let $L (H)$ denote the algebra of all bounded linear operators on a separable infinite dimensional complex Hilbert space $H$ into itself. Given $A \in L (H)$ , we define the elementary operator $Δ_{A} : L (H) ⟶ L (H)$ by $Δ_{A} (X) = A X A - X$ . In this paper we study the class of operators $A \in L (H)$ which have the following property: $A T A = T$ implies $A T^{*} A = T^{*}$ for all trace class operators $T \in C_{1} (H)$ . Such operators are termed generalized quasi-adjoints. The main result is the equivalence between this character and the fact that the ultraweak closure of the range of $Δ_{A}$ is closed...

On (n,k)-quasiparanormal operators

Jiangtao Yuan, Guoxing Ji (2012)

Studia Mathematica

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Let T be a bounded linear operator on a complex Hilbert space . For positive integers n and k, an operator T is called (n,k)-quasiparanormal if $| | T^{1 + n} (T^{k} x) {| |}^{1 / (1 + n)} | | T^{k} {x | |}^{n / (1 + n)} \geq | | T (T^{k} x) | |$ for x ∈ . The class of (n,k)-quasiparanormal operators contains the classes of n-paranormal and k-quasiparanormal operators. We consider some properties of (n,k)-quasiparanormal operators: (1) inclusion relations and examples; (2) a matrix representation and SVEP (single valued extension property); (3) ascent and Bishop’s property (β); (4)...

On operators with the same local spectra

Aleksandar Torgašev (1998)

Czechoslovak Mathematical Journal

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Let $B (X)$ be the algebra of all bounded linear operators in a complex Banach space $X$ . We consider operators $T_{1}, T_{2} \in B (X)$ satisfying the relation $σ_{T_{1}} (x) = σ_{T_{2}} (x)$ for any vector $x \in X$ , where $σ_{T} (x)$ denotes the local spectrum of $T \in B (X)$ at the point $x \in X$ . We say then that $T_{1}$ and $T_{2}$ have the same local spectra. We prove that then, under some conditions, $T_{1} - T_{2}$ is a quasinilpotent operator, that is $∥ {(T_{1} - T_{2})}^{n} ∥^{1 / n} \to 0$ as $n \to \infty$ . Without these conditions, we describe the operators with the same local spectra only in some particular cases.

On the norm-closure of the class of hypercyclic operators

Christoph Schmoeger (1997)

Annales Polonici Mathematici

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Let T be a bounded linear operator acting on a complex, separable, infinite-dimensional Hilbert space and let f: D → ℂ be an analytic function defined on an open set D ⊆ ℂ which contains the spectrum of T. If T is the limit of hypercyclic operators and if f is nonconstant on every connected component of D, then f(T) is the limit of hypercyclic operators if and only if $f (σ_{W} (T)) \cup z \in ℂ : | z | = 1$ is connected, where $σ_{W} (T)$ denotes the Weyl spectrum of T.

Besov spaces and 2-summing operators

M. A. Fugarolas (2004)

Colloquium Mathematicae

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Let Π₂ be the operator ideal of all absolutely 2-summing operators and let $I_{m}$ be the identity map of the m-dimensional linear space. We first establish upper estimates for some mixing norms of $I_{m}$ . Employing these estimates, we study the embedding operators between Besov function spaces as mixing operators. The result obtained is applied to give sufficient conditions under which certain kinds of integral operators, acting on a Besov function space, belong to Π₂; in this context, we also...

Conditions equivalent to C* independence

Shuilin Jin, Li Xu, Qinghua Jiang, Li Li (2012)

Studia Mathematica

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Let and be mutually commuting unital C* subalgebras of (). It is shown that and are C* independent if and only if for all natural numbers n, m, for all n-tuples A = (A₁, ..., Aₙ) of doubly commuting nonzero operators of and m-tuples B = (B₁, ..., Bₘ) of doubly commuting nonzero operators of , $S p (A, B) = S p (A) \times S p (B)$ , where Sp denotes the joint Taylor spectrum.

Separate and joint similarity to families of normal operators

Piotr Niemiec (2002)

Studia Mathematica

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Sets of bounded linear operators , ⊂ ℬ(H) (ℋ is a Hilbert space) are similar if there exists an invertible (in ℬ(H)) operator G such that $G^{- 1} \cdot \cdot G =$ . A bounded operator is scalar if it is similar to a normal operator. is jointly scalar if there exists a set ⊂ ℬ(H) of normal operators such that and are similar. is separately scalar if all its elements are scalar. Some necessary and sufficient conditions for joint scalarity of a separately scalar abelian set of Hilbert space operators are presented...

A new characterization of Anderson’s inequality in $C_{1}$ -classes

S. Mecheri (2007)

Czechoslovak Mathematical Journal

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Let $ℋ$ be a separable infinite dimensional complex Hilbert space, and let $ℒ (ℋ)$ denote the algebra of all bounded linear operators on $ℋ$ into itself. Let $A = (A_{1}, A_{2}, \dots, A_{n})$ , $B = (B_{1}, B_{2}, \dots, B_{n})$ be $n$ -tuples of operators in $ℒ (ℋ)$ ; we define the elementary operators $Δ_{A, B} ℒ (ℋ) \mapsto ℒ (ℋ)$ by $Δ_{A, B} (X) = \sum_{i = 1}^{n} A_{i} X B_{i} - X .$ In this paper, we characterize the class of pairs of operators $A, B \in ℒ (ℋ)$ satisfying Putnam-Fuglede’s property, i.e, the class of pairs of operators $A, B \in ℒ (ℋ)$ such that $\sum_{i = 1}^{n} B_{i} T A_{i} = T$ implies $\sum_{i = 1}^{n} A_{i}^{*} T B_{i}^{*} = T$ for all $T \in 𝒞_{1} (ℋ)$ (trace class operators). The main result is the equivalence between this property and the...

Multiple summing operators on $l_{p}$ spaces

Dumitru Popa (2014)

Studia Mathematica

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We use the Maurey-Rosenthal factorization theorem to obtain a new characterization of multiple 2-summing operators on a product of $l_{p}$ spaces. This characterization is used to show that multiple s-summing operators on a product of $l_{p}$ spaces with values in a Hilbert space are characterized by the boundedness of a natural multilinear functional (1 ≤ s ≤ 2). We use these results to show that there exist many natural multiple s-summing operators $T : l_{4 / 3} \times l_{4 / 3} \to l ₂$ such that none of the associated linear operators...

Modulation space estimates for multilinear pseudodifferential operators

Árpád Bényi, Kasso A. Okoudjou (2006)

Studia Mathematica

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We prove that for symbols in the modulation spaces $ℳ^{p, q}$ , p ≥ q, the associated multilinear pseudodifferential operators are bounded on products of appropriate modulation spaces. In particular, the symbols we study here are defined without any reference to smoothness, but rather in terms of their time-frequency behavior.

Absolutely continuous linear operators on Köthe-Bochner spaces

(2011)

Banach Center Publications

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Let E be a Banach function space over a finite and atomless measure space (Ω,Σ,μ) and let $(X, | | \cdot | |_{X})$ and $(Y, | | \cdot | |_{Y})$ be real Banach spaces. A linear operator T acting from the Köthe-Bochner space E(X) to Y is said to be absolutely continuous if $| | T (1_{A ₙ} f) {| |}_{Y} \to 0$ whenever μ(Aₙ) → 0, (Aₙ) ⊂ Σ. In this paper we examine absolutely continuous operators from E(X) to Y. Moreover, we establish relationships between different classes of linear operators from E(X) to Y.

A note on preservation of spectra for two given operators

Carlos Carpintero, Alexander Gutiérrez, Ennis Rosas, José Sanabria (2020)

Mathematica Bohemica

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We study the relationships between the spectra derived from Fredholm theory corresponding to two given bounded linear operators acting on the same space. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from Fredholm theory and other parts of the spectra corresponding to two given operators are preserved. As an application of our results, we give conditions for which the above mentioned spectra corresponding to two multiplication operators...

On operators Cauchy dual to 2-hyperexpansive operators: the unbounded case

Sameer Chavan (2011)

Studia Mathematica

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The Cauchy dual operator T’, given by $T {(T * T)}^{- 1}$ , provides a bounded unitary invariant for a closed left-invertible T. Hence, in some special cases, problems in the theory of unbounded Hilbert space operators can be related to similar problems in the theory of bounded Hilbert space operators. In particular, for a closed expansive T with finite-dimensional cokernel, it is shown that T admits the Cowen-Douglas decomposition if and only if T’ admits the Wold-type decomposition (see Definitions 1.1...

On a proof of the boundedness and nuclearity of pseudodifferential operators in $R^{n}$

Jan A. Rempała (1990)

Annales Polonici Mathematici

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